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so <- qs::qread("~/Desktop/analysis/snRNASeq_metabolic_changes_in_neurons_of_hippocampus/results/seurat_obj_int_harmony.clustering_osi_annotated_clean.qs")

Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio

so <- so@assays$RNA@layers$counts

var(counts |> as.vector())

[1] 3.027899

mean(counts |> as.vector())

[1] 0.172479

print(nb_params_df)

Error: object 'nb_params_df' not found

library(Matrix)
library(MASS)
library(ggplot2)

# Suppose 'counts' is your dgCMatrix (genes x cells)
# Optionally, filter out genes with very low total counts:
min_total <- 10  
gene_totals <- rowSums(counts)
keep_genes <- gene_totals >= min_total
counts_filtered <- counts[keep_genes, ]
gene_names <- rownames(counts_filtered)

# Initialize a data frame to collect the NB parameters and GoF statistic per gene:
results <- data.frame(Gene = character(),
                      mu = numeric(),
                      size = numeric(),
                      chi_sq = numeric(),
                      df = numeric(),
                      p_value = numeric(),
                      stringsAsFactors = FALSE)

for (i in seq_len(nrow(counts_filtered))) {
  gene_counts <- as.vector(counts_filtered[i, ])
  
  # Skip genes with no variability
  if (all(gene_counts == 0)) next
  
  fit <- try(fitdistr(gene_counts, densfun = "Negative Binomial"), silent = TRUE)
  if (inherits(fit, "try-error")) next
  
  size_est <- fit$estimate["size"]
  mu_est <- fit$estimate["mu"]
  
  total_cells <- length(gene_counts)
  max_count <- max(gene_counts)
  counts_seq <- 0:max_count
  
  # Build the observed frequency vector without expanding the full data:
  observed_freq <- numeric(max_count + 1)
  # Zeros (not stored explicitly in the sparse matrix)
  observed_freq[1] <- total_cells - sum(gene_counts > 0)
  if(max_count > 0) {
    observed_freq[-1] <- tabulate(gene_counts[gene_counts > 0], nbins = max_count)
  }
  
  # Calculate the expected probabilities and frequencies based on the NB model
  fitted_probs <- dnbinom(counts_seq, size = size_est, mu = mu_est)
  expected_freq <- fitted_probs * total_cells
  
  # Ensure expected frequencies are nonzero for chi-square computation:
  # (Sometimes, you may wish to combine bins with very low expected counts.)
  # For simplicity, we assume expected_freq are > 0.
  chi_sq <- sum((observed_freq - expected_freq)^2 / expected_freq)
  
  # Degrees of freedom:
  # Number of bins minus the number of estimated parameters (here 2) minus 1.
  df <- length(observed_freq) - 2 - 1
  
  # Compute p-value from the chi-square distribution:
  p_val <- pchisq(chi_sq, df = df, lower.tail = FALSE)
  
  # Append results to the dataframe:
  results <- rbind(results, data.frame(Gene = gene_names[i],
                                       mu = mu_est,
                                       size = size_est,
                                       chi_sq = chi_sq,
                                       df = df,
                                       p_value = p_val,
                                       stringsAsFactors = FALSE))
}

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producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs 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producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs producedWarning: NaNs produced

# View the summarized results:
print(results)

# Determine how many genes have an acceptable fit:
acceptable_fit <- sum(results$p_value > 0.05, na.rm=TRUE)
total_genes_fitted <- nrow(results)
cat("Proportion of genes well fit by NB:", acceptable_fit / total_genes_fitted, "\n")

Proportion of genes well fit by NB: 0.1103943 

library(dplyr)
results %>% filter(!is.nan(p_value))

# Load necessary libraries
library(ggplot2)
library(dplyr)

# Assume nb_params_df already exists. Here is a simulated example:
# For demonstration, we'll create a small example dataframe.
set.seed(42)


reults.red <- results %>% filter(!is.nan(p_value))

nb_params_df <- reults.red

# 1. Summary Statistics for Goodness-of-Fit
summary_stats <- nb_params_df %>% 
  summarise(
    total_genes = n(),
    mean_p_value = mean(p_value),
    median_p_value = median(p_value),
    prop_good_fit = mean(p_value > 0.05)  # proportion with p > 0.05 
  )
print(summary_stats)

# 2. Histogram of the p-values
p_hist <- ggplot(nb_params_df, aes(x = p_value)) +
  geom_histogram(binwidth = 0.05, fill = "skyblue", color = "black", boundary = 0) +
  labs(title = "Distribution of Goodness-of-Fit p-values",
       x = "p-value",
       y = "Number of Genes") +
  theme_minimal()
print(p_hist)

# 3. Scatter Plot: p-value vs. estimated mean (mu)
p_mu <- ggplot(nb_params_df, aes(x = mu, y = p_value)) +
  geom_point(color = "darkgreen", alpha = 0.7) +
  geom_hline(yintercept = 0.05, linetype = "dashed", color = "red") +
  labs(title = "p-value vs. Estimated Mean (mu)",
       x = "Estimated mean (mu)",
       y = "p-value") +
  theme_minimal()
print(p_mu)

# 4. Scatter Plot: p-value vs. size parameter (dispersion)
p_size <- ggplot(nb_params_df, aes(x = size, y = p_value)) +
  geom_point(color = "purple", alpha = 0.7) +
  geom_hline(yintercept = 0.05, linetype = "dashed", color = "red") +
  labs(title = "p-value vs. Estimated Dispersion Parameter (size)",
       x = "Estimated Dispersion (size)",
       y = "p-value") +
  theme_minimal()
print(p_size)

# 5. Optionally, you may also examine a combined plot
library(gridExtra)
grid.arrange(p_hist + scale_y_sqrt(), p_mu + scale_y_sqrt(), p_size + scale_y_sqrt(), ncol=1)

NA
NA
NA
NA
NA

library(Matrix)
library(MASS)
library(ggplot2)

# Suppose 'counts' is your dgCMatrix (genes x cells)
# Optionally, filter out genes with very low total counts:
min_total <- 10  
gene_totals <- rowSums(counts)
keep_genes <- gene_totals >= min_total
counts_filtered <- counts[keep_genes, ]
gene_names <- rownames(counts_filtered)

# Initialize a data frame to collect the NB parameters and GoF statistic per gene:
results <- data.frame(Gene = character(),
                      mu = numeric(),
                      size = numeric(),
                      chi_sq = numeric(),
                      df = numeric(),
                      p_value = numeric(),
                      stringsAsFactors = FALSE)

for (i in seq_len(nrow(counts_filtered))) {
  gene_counts <- as.vector(counts_filtered[i, ])
  
  # Skip genes with no variability
  if (all(gene_counts == 0)) next
  
  fit <- try(fitdistr(gene_counts, densfun = "Poisson"), silent = TRUE)
  if (inherits(fit, "try-error")) next
  
  size_est <- fit$estimate["size"]
  mu_est <- fit$estimate["mu"]
  
  total_cells <- length(gene_counts)
  max_count <- max(gene_counts)
  counts_seq <- 0:max_count
  
  # Build the observed frequency vector without expanding the full data:
  observed_freq <- numeric(max_count + 1)
  # Zeros (not stored explicitly in the sparse matrix)
  observed_freq[1] <- total_cells - sum(gene_counts > 0)
  if(max_count > 0) {
    observed_freq[-1] <- tabulate(gene_counts[gene_counts > 0], nbins = max_count)
  }
  
  # Calculate the expected probabilities and frequencies based on the NB model
  fitted_probs <- dnbinom(counts_seq, size = size_est, mu = mu_est)
  expected_freq <- fitted_probs * total_cells
  
  # Ensure expected frequencies are nonzero for chi-square computation:
  # (Sometimes, you may wish to combine bins with very low expected counts.)
  # For simplicity, we assume expected_freq are > 0.
  chi_sq <- sum((observed_freq - expected_freq)^2 / expected_freq)
  
  # Degrees of freedom:
  # Number of bins minus the number of estimated parameters (here 2) minus 1.
  df <- length(observed_freq) - 2 - 1
  
  # Compute p-value from the chi-square distribution:
  p_val <- pchisq(chi_sq, df = df, lower.tail = FALSE)
  
  # Append results to the dataframe:
  results <- rbind(results, data.frame(Gene = gene_names[i],
                                       mu = mu_est,
                                       size = size_est,
                                       chi_sq = chi_sq,
                                       df = df,
                                       p_value = p_val,
                                       stringsAsFactors = FALSE))
}

Error in data.frame(Gene = gene_names[i], mu = mu_est, size = size_est,  : 
  row names contain missing values

# Load required libraries
library(MASS)
library(fitdistrplus)
library(Matrix)
library(ggplot2)
library(reshape2)

# --- Step 1: Prepare the Data from dgCMatrix ---
# Suppose 'counts' is your dgCMatrix from Seurat.
# Example:
# counts <- GetAssayData(seurat_obj, slot = "counts")

# Calculate total entries, zeros, and summarize non-zero entries
total_entries <- nrow(counts) * ncol(counts)
nonzero_entries <- length(counts@x)
zero_entries <- total_entries - nonzero_entries

mean_nonzero <- mean(counts@x)
var_nonzero <- var(counts@x)

cat("Total entries:", total_entries, "\n")

Total entries: 37027800 

cat("Non-zero entries:", nonzero_entries, "\n")

Non-zero entries: 2282976 

cat("Zero entries:", zero_entries, "\n")

Zero entries: 34744824 

cat("Mean (non-zero):", mean_nonzero, "\n")

Mean (non-zero): 2.797453 

cat("Variance (non-zero):", var_nonzero, "\n")

Variance (non-zero): 41.76656 

# Determine maximum observed count (from non-zeros)
max_count <- max(counts@x)

# Create a frequency vector for counts 0 to max_count
freq <- numeric(max_count + 1)
freq[1] <- zero_entries  # zero count
freq[-1] <- tabulate(counts@x, nbins = max_count)
names(freq) <- 0:max_count

print(freq)

       0        1        2        3        4        5        6        7        8        9       10       11       12       13       14       15       16       17       18 
34744824  1593557   272936    99533    55921    39057    29635    24303    20063    16819    14577    12380    10814     9322     8026     7009     6275     5409     4917 
      19       20       21       22       23       24       25       26       27       28       29       30       31       32       33       34       35       36       37 
    4286     3779     3283     3053     2746     2445     2215     2041     1824     1720     1557     1402     1372     1242     1075      988      942      894      856 
      38       39       40       41       42       43       44       45       46       47       48       49       50       51       52       53       54       55       56 
     751      748      685      671      605      543      596      466      491      451      387      411      370      346      346      316      325      296      259 
      57       58       59       60       61       62       63       64       65       66       67       68       69       70       71       72       73       74       75 
     253      218      212      186      199      192      171      164      145      178      140      131      143      127      105      119      105       94      112 
      76       77       78       79       80       81       82       83       84       85       86       87       88       89       90       91       92       93       94 
     110       93       95       86       80       83       56       64       66       64       56       64       56       42       56       58       64       53       53 
      95       96       97       98       99      100      101      102      103      104      105      106      107      108      109      110      111      112      113 
      41       49       42       48       32       39       41       40       29       38       28       36       21       29       25       30       19       25       25 
     114      115      116      117      118      119      120      121      122      123      124      125      126      127      128      129      130      131      132 
      20       22       24       28       22       17       25       21       16       15       10       16       15       17       11       14       10       10       15 
     133      134      135      136      137      138      139      140      141      142      143      144      145      146      147      148      149      150      151 
       7        7       12       14        8       13        8        9        7       12        9        8        5        4        8        7       10       13        8 
     152      153      154      155      156      157      158      159      160      161      162      163      164      165      166      167      168      169      170 
       6        3       11        2        7        5        5        4        3        4        3        4        1        5        9        5        2        6        4 
     171      172      173      174      175      176      177      178      179      180      181      182      183      184      185      186      187      188      189 
       2        2        4        5        5        1        3        1        1        3        3        3        3        4        2        1        1        2        2 
     190      191      192      193      194      195      196      197      198      199      200      201      202      203      204      205      206      207      208 
       2        5        1        1        1        1        1        4        2        2        0        0        0        0        2        1        3        1        0 
     209      210      211      212      213      214      215      216      217      218      219      220      221      222      223      224      225      226      227 
       0        0        1        0        2        1        0        2        2        1        1        2        0        2        1        2        1        0        0 
     228      229      230      231      232      233      234      235      236      237      238      239      240      241      242      243      244      245      246 
       2        1        0        1        0        3        0        3        0        1        1        0        1        1        1        0        0        0        0 
     247      248      249      250      251      252      253      254      255      256      257      258      259      260      261      262      263      264      265 
       0        3        0        1        0        2        0        0        0        0        0        1        0        0        0        0        0        0        0 
     266      267      268      269      270      271      272      273      274      275      276      277      278      279      280      281      282      283      284 
       0        1        0        1        0        0        0        0        0        0        0        0        0        0        0        1        1        0        0 
     285      286      287      288      289      290      291      292      293      294      295      296      297      298      299      300      301      302      303 
       0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0 
     304      305      306      307      308      309      310      311      312      313      314      315      316      317      318      319      320      321      322 
       0        0        0        0        0        1        0        0        0        0        0        0        0        0        0        0        0        0        0 
     323      324      325      326      327      328      329      330      331      332      333      334      335      336      337      338      339      340      341 
       0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0 
     342      343      344      345      346      347      348      349      350      351      352      353      354      355      356      357      358      359      360 
       0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0 
     361      362      363      364      365      366      367      368      369      370      371      372      373      374      375      376      377      378      379 
       0        0        0        0        1        0        0        0        0        0        0        0        0        0        0        0        0        0        0 
     380      381      382      383      384      385      386      387      388      389      390      391      392      393      394      395      396      397      398 
       0        0        0        0        1        0        0        0        0        0        0        1        0        0        0        0        0        0        0 
     399      400      401      402      403      404      405      406      407      408      409      410      411      412      413      414      415      416      417 
       0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0        0 
     418      419 
       0        1 

# (Optional) Reconstruct a full vector from freq if memory allows (for fitting/testing):
all_counts <- rep(0:max_count, times = freq)

# --- Step 2: Fit a Poisson Model ---
# Use fitdistr() to estimate the Poisson parameter lambda
pois_fit <- fitdistr(all_counts, densfun = "Poisson")
print(pois_fit)

      lambda   
  1.724790e-01 
 (6.825024e-05)

# The Poisson parameter is "lambda"
lambda_est <- pois_fit$estimate["lambda"]

# --- Step 3: Compute Expected Frequencies Under Poisson ---
# Create a sequence of counts (from 0 to max_count)
counts_seq <- 0:max_count

# Compute Poisson PMF for each count and scale to get expected frequencies
fitted_probs <- dpois(counts_seq, lambda = lambda_est)
total_obs <- length(all_counts)
expected_freq <- fitted_probs * total_obs

# Observed frequencies (as computed above)
observed_freq <- as.numeric(table(factor(all_counts, levels = counts_seq)))

# Create a dataframe for plotting
df <- data.frame(
  Count = counts_seq,
  Observed = observed_freq,
  Expected = expected_freq
)

# --- Step 4: Visualization with ggplot2 ---
# Melt the dataframe to long format for ggplot2
df_melted <- melt(df, id.vars = "Count", variable.name = "Type", value.name = "Frequency")

# Create the plot:
ggplot(df_melted, aes(x = Count, y = Frequency, fill = Type)) +
  geom_bar(stat = "identity", position = "dodge", color = "black", alpha = 0.7) +
  scale_fill_manual(values = c("Observed" = "skyblue", "Expected" = "red")) +
  labs(title = "Observed vs Expected Frequencies (Poisson Fit)",
       x = "Count",
       y = "Frequency (square-root scale)") +
  theme_minimal() +
  scale_y_sqrt() +
  xlim(-1, 10)

freq

   [1] 1131587421   44035942   14688793    6375839    3302039    1930523    1235210     847755     612284     461604     358807     287885     234672
  [14]     195140     165146     142135     123007     107416      94747      84349      75221      67761      60961      55677      50659      46293
  [27]      42688      39039      35943      33414      31012      29193      26979      25303      23617      22162      20755      19271      18218
  [40]      17338      16417      15374      14689      13756      13008      12486      12016      11171      10554      10080       9651       9284
  [53]       8782       8379       7963       7606       7386       7065       6805       6381       6201       5973       5721       5407       5303
  [66]       5241       4941       4727       4633       4324       4188       4006       3902       3868       3758       3559       3403       3272
  [79]       3192       3096       2928       2902       2779       2789       2644       2569       2487       2396       2285       2229       2198
  [92]       2121       2140       2044       1941       1899       1874       1797       1725       1699       1611       1653       1668       1493
 [105]       1446       1438       1488       1415       1383       1344       1245       1201       1274       1171       1171       1161       1088
 [118]       1039       1031       1112        993        988        997        929        933        837        914        865        872        864
 [131]        812        852        750        759        753        701        737        716        639        642        673        625        628
 [144]        623        652        624        582        546        561        545        559        551        521        509        512        531
 [157]        456        474        421        452        448        462        453        404        429        436        368        430        395
 [170]        403        397        371        340        385        379        373        340        336        298        332        328        356
 [183]        312        316        291        291        279        289        301        259        288        279        277        250        234
 [196]        228        239        230        251        263        227        238        211        228        226        207        216        192
 [209]        215        228        187        194        198        203        212        215        204        191        167        180        174
 [222]        170        189        171        169        201        158        172        185        181        157        158        164        157
 [235]        152        164        149        159        137        146        140        136        148        142        139        140        140
 [248]        142        131        119        135        135        125        126        123        124        138        111        118        137
 [261]        117        117        119        132        111        106        114        105        128        115        113        105         94
 [274]        109         92        101        105        110         99         90         92         83         98         92         94        114
 [287]         74         82         97         99         94         94         75        103         82         79         66         82        105
 [300]         84         80        101         90         76         82         54         70         70         66         77         77         69
 [313]         71         66         68         78         58         63         80         72         73         74         69         70         71
 [326]         71         86         66         57         53         62         62         61         67         64         61         70         68
 [339]         59         65         63         60         59         58         62         58         72         43         52         57         57
 [352]         53         55         48         51         46         51         44         56         49         64         40         39         54
 [365]         58         46         33         43         46         40         40         53         46         53         50         39         43
 [378]         56         42         46         44         43         37         53         48         48         46         33         34         43
 [391]         46         37         40         43         37         33         42         39         27         40         42         44         43
 [404]         39         46         37         43         34         25         38         39         27         27         27         33         32
 [417]         28         34         37         33         28         25         29         24         29         35         25         27         38
 [430]         24         33         22         26         24         26         29         39         17         32         22         19         26
 [443]         28         19         23         31         30         21         35         34         21         25         26         40         31
 [456]         17         16         32         33         16         24         23         21         22         30         27         21         21
 [469]         19         30         21         25         21         24         23         28         17         26         17         24         28
 [482]         25         24         20         24         21         25         22         22         15         20         21         29         19
 [495]         16         21         22         21         24         23         20         27         23         30         18         18         14
 [508]         15         12         20         17         22         18         17         24         17         12         15         24         17
 [521]         21         16         16         20         19         15         20         26         23         17         26         17         14
 [534]         12         12         17         13         14         25         13         18         17         15         18         12         18
 [547]         20         16         19         15         11         17         21         17         22         19         12         23          9
 [560]          8         15         17         16         16         13         12         22          9          5         16         23          7
 [573]         21         14         24         17         13         18          9         13         12         11         12         14         15
 [586]         12         13         17         14         14         14         13         11         14         13         11         13         20
 [599]         13         13          9         15         15         17         13         17          8         12         15         17         15
 [612]         16         14         13         14         11         15          7         19         15         20         15         12         15
 [625]         17          9         18         12         14         18         14         14         15         12         14         15         10
 [638]         12          6         12         12         19         15         17         16         14         20         11         17         10
 [651]         12         13         12         12         19         12         18         10          9         13          9         19         14
 [664]         11         13         21         19         15          8         11         18         18         11         14         12         16
 [677]         14         14         14         20         13         11         16         17         24         17         10         16         12
 [690]          8         19         11          9         13         11         19         10          9         18         12         13          8
 [703]         17         14         20         12         14          4         20         20          7         12         14          9         10
 [716]         16         10          7         11          8          7         15          9         13         13         14          9         12
 [729]         14         16         13         16         12          9         10         10         11          5         12         10         13
 [742]          8         12         16          8         11          9         12         12         13         12          9         21         10
 [755]          8         14         14         11         14          5         11         10         13         18          9         13         11
 [768]         17         15         15          8         12         12         14          9         14         14         12          8         12
 [781]         15         16         11         12          8         18         10          9          3         15         14         12         11
 [794]         10         16         16         12          8          8         15         18          6         10         13          5         13
 [807]         14          7         13          9          7         12         13         10          6          9          9         10         14
 [820]         20          8          9         10         12         13         12         11         14          4         10         19          8
 [833]         14          0          8         12          8          9         17          9         10         10         10          8          9
 [846]          7         12         10          8          7          6         11         13          9         12          6          7         13
 [859]          8         12         14          8          5         10         11          8         12          6          7         13          5
 [872]         13          7         10         12         15          7          8         11         10         12         11         10         13
 [885]         12          5         10          9         15         10          4          9         10         14          8          8          7
 [898]          9         10          7          8          5          8          8          9         10          7         11          7         10
 [911]          9          6         10          5          9          6         13          6         15          7          7          8         10
 [924]         15          4          6          8          9          7          9         12          6         13          6          8          9
 [937]          7          5          8         10          7         12         17          7         11          5          4          9          7
 [950]         11          6          7          5          8         13         11          5         11          5          7         12         14
 [963]          6          5          9          9         11         14         13          5         10          5          8          9         11
 [976]          3          8         11          9          8         10          7          8          8         13          9          1          9
 [989]         10          8          8          5         17         10          5         11          6          9         16          9
 [ reached getOption("max.print") -- omitted 3868 entries ]

library(SeuratData)

Registered S3 method overwritten by 'data.table':
  method           from
  print.data.table     
Registered S3 method overwritten by 'htmlwidgets':
  method           from         
  print.htmlwidget tools:rstudio
── Installed datasets ──────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────────── SeuratData v0.2.2.9001 ──
✔ kidneyref 1.0.2                                                                       ✔ pbmcref   1.0.0
✔ panc8     3.0.2                                                                       ✔ stxKidney 0.1.0
✔ pbmc3k    3.1.4                                                                       

────────────────────────────────────────────────────────────────────────────────────── Key ─────────────────────────────────────────────────────────────────────────────────────
✔ Dataset loaded successfully
❯ Dataset built with a newer version of Seurat than installed
❓ Unknown version of Seurat installed

InstallData("pbmc3k")

Warning: The following packages are already installed and will not be reinstalled: pbmc3k

pbmc3k <- Seurat::UpdateSeuratObject(pbmc3k)

Validating object structure
Updating object slots
Ensuring keys are in the proper structure
Warning: Assay RNA changing from Assay to AssayEnsuring keys are in the proper structure
Ensuring feature names don't have underscores or pipes
Updating slots in RNA
Validating object structure for Assay ‘RNA’
Object representation is consistent with the most current Seurat version

counts <- pbmc3k@assays$RNA@counts